Multitype Branching Processes

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Multitype Branching Processes

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Author : Charles J. Mode
language : en
Publisher:
Release Date : 1971

Multitype Branching Processes written by Charles J. Mode and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Mathematics categories.

Multitype Branching Processes

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Author : Charles Mode
language : en
Publisher:
Release Date : 1971

Multitype Branching Processes written by Charles Mode and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Branching processes categories.

Workshop On Branching Processes And Their Applications

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Author : Miguel González
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-03-02

Workshop On Branching Processes And Their Applications written by Miguel González and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-03-02 with Mathematics categories.

One of the charms of mathematics is the contrast between its generality and its applicability to concrete, even everyday, problems. Branching processes are typical in this. Their niche of mathematics is the abstract pattern of reproduction, sets of individuals changing size and composition through their members reproducing; in other words, what Plato might have called the pure idea behind demography, population biology, cell kinetics, molecular replication, or nuclear ?ssion, had he known these scienti?c ?elds. Even in the performance of algorithms for sorting and classi?cation there is an inkling of the same pattern. In special cases, general properties of the abstract ideal then interact with the physical or biological or whatever properties at hand. But the population, or bran- ing, pattern is strong; it tends to dominate, and here lies the reason for the extreme usefulness of branching processes in diverse applications. Branching is a clean and beautiful mathematical pattern, with an intellectually challenging intrinsic structure, and it pervades the phenomena it underlies.

Multitype Branching Processes In Random Environments

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Author : Edward Wells Weissner
language : en
Publisher:
Release Date : 1970

Multitype Branching Processes In Random Environments written by Edward Wells Weissner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Markov processes categories.

Consider the k-type Galton-Watson process. The work removes the restrictive assumption that particles of the same type always divide in accordance with the same probability generating function (p.g.f.). Instead, it is assumed that at each unit of time, Nature chooses a k-vector of p.g.f.s from a class of k-vectors of p.g.f.s., independently of the population, past and present, and the previously selected k-vectors, which is then assigned to the present population. Each particle of the present population then splits or disintegrates, independently of the others, in accordance with the p.g.f. assigned to its classification. This process is called a multitype branching process in a random environment (MBPRE). The work gives some necessary and some sufficient conditions for almost certain extinction of the MBPRE when there are at least two particle classifications. To obtain these results, Jensen's inequality, the dual process suggested by Smith and Wilkinson, and some results on products of random matrices are used. Since the theorems require the user to evaluate limits of sequences of products of random arrays, some corollaries are included which involve simpler, albeit less general, conditions. (Author).

Branching Processes In Biology

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Author : Marek Kimmel
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-05-26

Branching Processes In Biology written by Marek Kimmel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-26 with Mathematics categories.

This book introduces biological examples of Branching Processes from molecular and cellular biology as well as from the fields of human evolution and medicine and discusses them in the context of the relevant mathematics. It provides a useful introduction to how the modeling can be done and for what types of problems branching processes can be used.

Branching Processes

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Author : Krishna B. Athreya
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Branching Processes written by Krishna B. Athreya and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

The purpose of this book is to give a unified treatment of the limit theory of branching processes. Since the publication of the important book of T E. Harris (Theory of Branching Processes, Springer, 1963) the subject has developed and matured significantly. Many of the classical limit laws are now known in their sharpest form, and there are new proofs that give insight into the results. Our work deals primarily with this decade, and thus has very little overlap with that of Harris. Only enough material is repeated to make the treatment essentially self-contained. For example, certain foundational questions on the construction of processes, to which we have nothing new to add, are not developed. There is a natural classification of branching processes according to their criticality condition, their time parameter, the single or multi-type particle cases, the Markovian or non-Markovian character of the pro cess, etc. We have tried to avoid the rather uneconomical and un enlightening approach of treating these categories independently, and by a series of similar but increasingly complicated techniques. The basic Galton-Watson process is developed in great detail in Chapters I and II.

Limiting Distributions For Critical Multitype Branching Processes

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Author : T. W. Mullikin
language : en
Publisher:
Release Date : 1961

Limiting Distributions For Critical Multitype Branching Processes written by T. W. Mullikin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with Branching processes categories.

Multitype Branching Processes In Varying And Randon I E Random Environment

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Author : Harry Cohn
language : en
Publisher:
Release Date : 1990

Multitype Branching Processes In Varying And Randon I E Random Environment written by Harry Cohn and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Branching processes categories.

Multitype Branching Processes

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Author : Steven Goldstein
language : en
Publisher:
Release Date : 1988

Multitype Branching Processes written by Steven Goldstein and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with categories.

Critical Age Dependent Branching Processes

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Author : Martin Ivan Goldstein
language : en
Publisher:
Release Date : 1969

Critical Age Dependent Branching Processes written by Martin Ivan Goldstein and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Branching processes categories.